Graduate Seminar

Location:  ED 114

Speaker: Sofia Medina Varela

MSc Student supervised by Doug Farenick

Title: The Kadison Similarity Problem

 Abstract:

In 1955 Richard Kadison posed the following question: "Is every bounded homomorphism from a C\(^\ast\)-algebra into \(B(\mathcal H)\) similar to a \(\ast\)-representation?". This is known as the Kadison Similarity Problem, and it remains open. Between 1981 and 1983, Haagerup, Hadwin, and Wittstock proved characterizations for such a bounded homomorphism to have a positive answer. Earlier this year, Fang, et al, showed some interesting results when the range is instead taken to be a von Neumann algebra \(M\subseteq B(\mathcal{H})\). In this talk we will discuss the above characterizations and recent results, as well as potential formulations of the similarity problem in the category of operator systems.